Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
676 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#10587561 | C2 | semidirect |
| 3. C2×C4×Dic34 | C2 | semidirect |
| 4. #11762727 | C2 | semidirect |
| 5. #11762711 | C2 | semidirect |
| 6. #11762710 | C2 | semidirect |
| 7. C4×C4⋊C4×C17 | C2 | semidirect |
| 40. C2×Dic34 | D4 | semidirect |
| 88. C4×C17 | #124 | semidirect |
| 97. C4×C4⋊C4 | D17 | semidirect |
| 120. C17 | #2548 | semidirect |
| 185. C4 | #10587561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587560 | 2 |
| C2×#10587561 | 2 |
| C2×C4×Dic34 | 2 |
| #11762727 | 2 |
| #11762711 | 2 |
| #11762710 | 2 |
| C4×C4⋊C4×C17 | 2 |
| #2548 | 17 |